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inn [45]
3 years ago
5

Someone please explain step by step.

Mathematics
1 answer:
dolphi86 [110]3 years ago
6 0

Answer:

{10}^{th}  \: term  =  \frac{5}{512}

Step-by-step explanation:

geometric progression formula:

{n}^{th} \:  term  = ar ^{n - 1}

given:

common ratio, r = 1/2

first \: term \:  = 5

1) find the value of a

{n}^{th}  \: term \:  = a {r}^{n - 1}

we're finding the 1st term, so substitute 1 into n:

{1}^{st}  \: term  = a( \frac{1}{2} ) {}^{1 - 1}

first term is 5. so we substitute 5 into the equation:

5 = a(1)

a = 5

2) find the 10th term

we're finding the 10th term, so substitute 10 into the equation and don't forget to substitute 5 into a:

{10}^{th}  \: term  = 5( \frac{1}{2} ) {}^{10 - 1}

{10}^{th}  \: term  = 5( \frac{1}{512} )

{10}^{th}  \: term =  \frac{5}{512}

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8 0
3 years ago
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Helen [10]

Answer:

1. ΔUJN ≅ ΔUGN by SAS rule of congruency

2. Side Angle Side Rule of congruency

3. JN ≅ GN, ∠JUN ≅ ∠NUG, ∠UNJ ≅ ∠UNG, NU ≅ NU

4. UN bisects angle ∠JUG and UN bisects segment JG

Step-by-step explanation:

The given figure consists of three triangles

1. ΔUJN, 2. ΔUGN, and 3. ΔUJG

Whereby segment UN is perpendicular to segment JG, we have;

ΔUJN and ΔUGN are right triangles

∴ ∠UNJ = ∠UNG = 90° by definition of segment UN being perpendicular to segment JG

NU ≅ NU by reflexive property

Whereby UN bisects ∠JUG and segment JG, we have;

JN = GN by definition of a bisected segment

Therefore, we have;

1. ΔUJN ≅ ΔUGN by SAS rule of congruency

2. Side Angle Side Rule of congruency

3. JN ≅ GN, ∠JUN ≅ ∠NUG, ∠UNJ ≅ ∠UNG, NU ≅ NU

4. UN bisects angle ∠JUG and UN bisects segment JG

7 0
3 years ago
Evaluate Integral: 2sin(2x) from 0, pi/2
Neko [114]
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= -cos(2*pi/2)-(-cos0)
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3 years ago
Ten less than half of a number(x) is 6.
Likurg_2 [28]

Answer:

x = 32

Step-by-step explanation:

Given the following data;

Unknown number = x

Translating the word problem into an algebraic equation, we have;

\frac {x}{2} - 10 = 6

Lowest common denominator (LCD) = 2

We multiply all through by 2;

2* \frac {x}{2} - 2*10 = 2*6

x - 20 = 12

x = 12 + 20

x = 32

Therefore, the unknown number is 32.

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3 years ago
Determine whether the lines are parallel or perpendicular or neither. 2x=y−10 and y=−2x
MrRa [10]

Put the first equation in slope-intercept form, or y = mx + b. Start by subtracting y from both sides.

2x - y = -10, subtract 2x from both sides.

-y = -10 - 2x

Divide both sides by negative one.

y = 10 + 2x

To find the slope when the equations are in slope-intercept form you look at the coefficient of x. The first equation has the slope of 2 (which we just found), and the second equation has the slope of -2.

Parallel lines have the same slope and perpendicular lines have opposite reciprocal slopes. Since 2 and -2 are neither of these, your answer is neither.

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3 years ago
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